$z=73i-32$ What is the real part of $z$ ?
Solution: Background Complex numbers are numbers of the form $z={a}+{b}i$, where $i$ is the imaginary unit and ${a}$ and ${b}$ are real numbers. [What is the imaginary unit?] The real part of $z$ is denoted by $\text{Re}(z)={a}$. The imaginary part of $z$ is denoted by $\text{Im}(z)={b}.$ Finding the Real and Imaginary Parts of $z$ In this case, $z={73}i-{32}$ is of the form ${b}i+{a}$, where ${a}={-32}$ and ${b}={73}$. Therefore: $\text{Re}(z)={a}={-32}$. $\text{Im}(z)={b}={73}$. Summary The real part of $z$ is ${-32}$. The imaginary part of $z$ is ${73}$.